Why does UDP have a length field in the header and TCP does not?

Question

According to TCP/IP Illustrated Volume 1, the length field is redundant. That's all Stevens says on the matter.

I personally believe it was to make the UDP header length (in bits) divisible by 32 :)

There is a 96 bit pseudo header conceptually prefixed to the TCP header that contains the information already.

The checksum field description from this source gives the answer:

Checksum: 16 bits

The checksum field is the 16 bit one's complement of the one's complement sum of all 16 bit words in the header and text. If a segment contains an odd number of header and text octets to be checksummed, the last octet is padded on the right with zeros to form a 16 bit word for checksum purposes. The pad is not transmitted as part of the segment. While computing the checksum, the checksum field itself is replaced with zeros.

The checksum also covers a 96 bit pseudo header conceptually prefixed to the TCP header. This pseudo header contains the Source Address, the Destination Address, the Protocol, and TCP length. This gives the TCP protection against misrouted segments. This information is carried in the Internet Protocol and is transferred across the TCP/Network interface in the arguments or results of calls by the TCP on the IP.

      +--------+--------+--------+--------+
      |           Source Address          |
      +--------+--------+--------+--------+
      |         Destination Address       |
      +--------+--------+--------+--------+
      |  zero  |  PTCL  |    TCP Length   |
      +--------+--------+--------+--------+

The information is not needed at the TCP level since TCP is a stream based protocol.